Brown the ground chicken in a large skillet over medium-high heat. Flip and push to one side of the skillet. Add the olive oil and onion, celery, and carrot. Stir everything together, breaking the chicken apart.
Once fully cooked, add the flour, salt garlic powder, and pepper. Stir until no flour is visible. Add the tomato paste and cook until fragrant.
Add the broth, vinegar, Worcestershire, thyme, and bay leaves. Bring up to a boil before reducing the heat to a medium-low simmer. Cook for 10-15 minutes, stirring occasionally, until the meat mixture thickens to resemble a gravy or meat sauce.
Turn off the heat and set aside while you microwave the mashed potatoes. Add the potatoes on top of the meat mixture, followed by the grated parmesan. Drizzle 1/2 tablespoon of olive oil over the top.
Bake at 350ºF for 35-45 minutes until the top is golden brown. For best results, let the pie cool for 5-10 minutes before serving. Top with fresh parsley and serve.